대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제59권2호
  • /
  • Pages.285-301
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  • 2022
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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RANDOM SAMPLING AND RECONSTRUCTION OF SIGNALS WITH FINITE RATE OF INNOVATION

  • Jiang, Yingchun (School of Mathematics and Computational Science Guilin University of Electronic Technology) ;
  • Zhao, Junjian (School of Mathematical Sciences TianGong University)
  • 투고 : 2020.10.28
  • 심사 : 2021.11.18
  • 발행 : 2022.03.31
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초록

In this paper, we mainly study the random sampling and reconstruction of signals living in the subspace Vp(𝚽, 𝚲) of Lp(ℝd), which is generated by a family of molecules 𝚽 located on a relatively separated subset 𝚲 ⊂ ℝd. The space Vp(𝚽, 𝚲) is used to model signals with finite rate of innovation, such as stream of pulses in GPS applications, cellular radio and ultra wide-band communication. The sampling set is independently and randomly drawn from a general probability distribution over ℝd. Under some proper conditions for the generators 𝚽 = {𝜙λ : λ ∈ 𝚲} and the probability density function 𝜌, we first approximate Vp(𝚽, 𝚲) by a finite dimensional subspace VpN (𝚽, 𝚲) on any bounded domains. Then, we prove that the random sampling stability holds with high probability for all signals in Vp(𝚽, 𝚲) whose energy concentrate on a cube when the sampling size is large enough. Finally, a reconstruction algorithm based on random samples is given for signals in VpN (𝚽, 𝚲).

키워드

과제정보

This work is supported by the National Natural Science Foundation of China (No. 11661024) and the Guangxi Natural Science Foundation (Nos. 2020GXNSFAA159076, 2019GXNSFFA245012), Natural Science Foundation of Tianjin City (No. 18JCYBJC16300), Guangxi Science and Technology Project (No. 2021AC06001), Guangxi Key Laboratory of Cryptography and Information Security (No. GCIS201925), Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation.

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